The Horatio Principle, SRH, Russell’s Paradox and Zermelo

ZFC does not assume that, for every property, there is a set of all things satisfying that property. Rather, it asserts that given any set X, any subset of X definable using first-order logic exists. The object R discussed above cannot be constructed in this fashion, and is therefore not a ZFC set. In some extensions of ZFC, objects like R are called proper classes. ZFC is silent about types, although some argue that Zermelo's axioms tacitly presuppose a background type theory.

In ZFC, given a set A, it is possible to define a set B that consists of exactly the sets in A that are not members of themselves. B cannot be in A by the same reasoning in Russell's Paradox. This variation of Russell's paradox shows that no set contains everything.

[http://en.wikipedia.org/wiki/Russell's_paradox]

This could well be the style of proof I’m looking for with the SRH. The above says that for a set A we can define B = {x in A & x not in x}. Thus if B is in A then there is Russell’s Paradox so B is not in A. This assumes the Zermelo axiom that existence can only be asserted for subsets of a given set, not for subsets of “all things”.

Freedom, Ayn Rand, Individualism, Selfish Interests, Addiction

Technorati Tags: Freedom,Ayn Rand,Individualism,Selfish Interests,Addiction

Dissenters of the traditional view that we ought to sacrifice ourselves for other people might consider this post simply a dogmatic reiteration of the “traditional” view. But if we fear whether our thoughts are fashionable or old-fashioned we most certainly reduce our freedom. I’d rather ignore current fads and simply say things as they are.

Individualists like Ayn Rand, Sartre, Nietzsche speak a lot about “freedom”. So what is so free about “freedom”. A prince in a Hollywood film says “True I can have anything I want, but like all men I can’t chose what I want”. Thus we often end up wanting things that really it is best for us if we didn’t want. This is the whole naivety of the Individualist view. It is also said traditionally that it takes a great man to command an army but only the greatest man can command himself. This is the essence of the Religions: the learning to be master of our self. Shakespere’s Othello is a model of how lack of self mastery makes us to weakest of men. We need only see an addict swearing they are in control and demanding “freedom” to do what they want to see the weakness of this type of thinking. A asked a Buddhist once what was wrong with the ego he said that the ego works in its own interests even at the expense of the whole self. This has turned out to be a very deep understanding of the problem; far deeper than the allegory of the Devil used by religions. The drug addict, or anyone with a compulsive habit, finds that what they want to do, indeed need to do, is actually bad for them.

“Simply look at how many people have died in the name of Freedom—it is far more than all other causes added together.”

However because the wish to do it is so strong they are prepared to ignore the side effects. I once saw a film of a smoking addict in a wheel chair who had lost both legs due to blood clots. The interviewer said that clearly the smoking was killing him, he said he didn’t care and was prepared to die bit by bit. That is a strong desire. Everything was sacrificed for the need to smoke. We would argue that at least a more balanced life with a mixture of other activities would be more worthwhile. But the addict won’t see this and their addiction and need to do what they want will be more valuable to them than even their own life. This is the nihilism and meaninglessness at the root of self-interest, exactly what the SRH says. In any case it is clear to see here the extreme individualist sacrificing everything here for a desire, when originally he wanted to be free from sacrifice altogether.

So “freedom” where does it go wrong?

In a world where we really do determine our own future and every road is open what do we do? Are we like the Dice Man and freely pick 6 random possibilities like: {Eat, Sleep, TV, Sex, Defecate, Kill ourselves}. With complete unconditional indifference to the future and complete “freedom” from the Past we roll the dice and do whatever is says. Except we are deciding to then having our future dictated by a dice. What if we decide to obey a new die: {obey the dice, don’t obey the die}. Decide to roll that a few times and we’re back to square one!

Alternatively Individualists put emphasis on our “will” (Nietzsche/ Sartre) or “desires” (Rand). The idea is that we are what we do/will/desire. For Sartre it is our choices that make/build/design the future. For Nietzsche it is our inexorable innate will to supremacy that drives our very action. For Ayn Rand it seems (and I have only caught whiff of her philosophy) it is our desires/wishes which determine our future. Hers is by far the most juvenile and trivial philosophy: we are slaves to our own desire then exactly as in the above paragraph. She preaches the worst kind of imprisonment and her followers walk in the opposite direction to freedom. As religions endlessly try to persuade people, the Devil is most cunning and will promise you everything so that you submit your soul to him—he is the most expert door to door salesman. As far as I can see it Ayn Rand basically says give into his demands and do whatever you want even if it is bad for you.

Sartre and Nietzsche are however better versions of Individualism but they still seem to suffer from a lack of freedom. To say that we are free to exercise our will to power is to say that we are a slave to power. My personal life at the moment is exactly the will to gain power over the will to power so that I no longer need to be viewed as successful or worth something. Isn’t this the contradictory zenith of Nietzsche’s philosophy—freedom even from this universal principle? With Sartre my problem is that any choice we make to be successful must take into account our environment. If I wish to buy some food I have no choice but to go to a food shop. If you analyse why I wish to have food it is because my stupid body needs energy. I have no choice over this. I may chose to sit down and die from starvation, but really this is my stupid mind rebelling against having to do things which becomes just another thing I feel compelled to do. Whichever way I turn I find myself embedded “in a world”—immersed as a friend once called it. When we are underwater we cannot move without displacing water around us. So it is with the world we cannot move without the world moving with us—there is no escape, indeed even thoughts of escape are movements in the water!

No freedom is a complete misnomer. Even the search for freedom binds us to an activity that becomes a bore and an oppressive tyrant. Simply look at how many people have died in the name of Freedom—it is far more than all other causes added together and squared. Freedom begins when we accept where we are rather than confronting it and trying to change it. If we are trying to change it then we are just slave to another force from within. What proponents of freedom are really responding to is the notion of a sovereign self: it makes a difference whether the tyrant is from within or from without. That is the next discussion. Historically Freedom is an obvious major issue in the West because we are in opposition to our history of Slavery. Like a guilty man we are particularly sensitive to slavery and rather over do the freedom angle. What we ought to see immediately though is that without the possibility of slavery how can there be freedom? When we speak of freedom we are really admitting that slavery still exists.

Most of this is blogged already in this blogroll. The puzzle from ancient Greece of whether the Argo returning from its 10 year quest was really the same boat that left since every plank of wood had been replaced at least once on the journey. So it is with us. Which thought, which desire, which body part, which possession is really us? Are they all us? If so do we lose a bit of ourselves when we lose one? If we do then where is that bit of myself in my car, or in my hair on the barbershop floor? Rubbish it is just a car, it is just hair. There is nothing about me in them either on the shop floor on in my possession. It is the same as a piece being in check in a game of chess. It isn’t really in check unless you understand the rules of the game: we simply make it up. That is all the self is: something we make up. The search for freedom is just something we make up; and we can just as easily unmake it! If we were truly free we would be able to unmake it… but we can’t! Especially when we believe in a philosophy that is based upon that very belief in self. Free yourself; stop believing.

Like all things, Individualists are right about something however. It is correct that we take responsibility for what we do and we do find our self so that we can become master it. It is not good enough to just follow the crowd like sheep, any more than it is to simply switching off saying it doesn’t matter it’s all just make believe. This just sends us from one make-believe world into another where everything is make-believe—we start believing that everything is make-believe! It is not that easy. What does “make believe” mean anyway? Ayn Rand started off in the right direction, she saw the irony is forming a “group of believers in Individualism” but the Devil is strong and she fell foul very quickly of her own philosophy believing that this meant that she should follow her desires. She ironically became to a slave to herself as she ran from what she perceived was others becoming slaves of the mass. True Freedom ain’t so simple which is why mankind has been pursuing it for 10 thousand years and why so very few have ever achieved it.

Loren Carpenter

Adam Curtis’ new documentary features an experimental game of Pong operated by the ratio of red and green paddles held up by each half of an audience. The experiment was performed on an minimally instructed audience by Loren Carpenter (of Pixar fame) in 1991.

Quote from Adam Curtis,

"It was like a switch went in my head," Curtis says. "Carpenter saw it as a world of freedom with order. But I suddenly saw it as the opposite – like old film of workers toiling in a factory. They weren't free – they looked like disempowered slaves locked to a giant machine screen. It was a video game, which made it fun, but it still made me wonder whether power had really gone away in these self-organising systems, or if it was just a rebranding. So we became happy components in systems – and our job is to make those systems stable."
http://www.guardian.co.uk/tv-and-radio/2011/may/06/adam-curtis-computers-documentary

Written up here.
http://www.capatcolumbia.com/reading%20packet/Out%20of%20Control.pdf

Comment:
Curtis’ analysis is naive. We are not individuals either free to pursue our “own” interests or individual caught within the web of group interaction… we aren’t individual at all! Each of us is the accumulation of interactions just as much as the game is the accumulation of individual interacting. It is fractal and hierarchical.

To reductio ad absurdum Curtis I need only point out that he is trapped within the confines of the collective understanding of English. Where is his “individual” if he frees himself from language? Where is the freedom in even generating media that necessarily requires an audience?

The experiment is interesting I need pursue it more. It may be useful to understand the stock market also especially the frequency of oscillations and size of movements induced by slower feedback (less volume), and the fact that bird flocks have faster response rates than individual birds so that groups adapt to signals faster than individuals! Really suggests that there are emergent “entities” (which is an oxymoron since we are discussing the dissolution of selves into groups so what sense in making groups just new individuals).

Technorati Tags: loren carpenter,adam curtis

Multiverse & SRH

Think I had it in for the Multiverse concept at some stage; obvious change of mind now. Multiverse is the concept that instead of quantum waves collapsing into discrete recordable events, instead they create new universes, one for each event. David Deutsch champions this idea in connection with quantum computing where the possibilities in many universes can be utilised to compute results in this universe.

My problem with this is—after recent developments in the SRH—just linguistic. A universe suggests already that there is nothing outside it. To coin the term “multiverse” is completely oxymoronic and contradicts the meaning of universe. What quantum theory has opened is the realisation that what we thought was the limit of the universe is really just the limit of one bubble of space-time and other bubbles might exist. The “multiverse” is just a name for our better understood universe. For analogy how absurd to call the other planets multiverses in the days when the universe extended to just this planet and its atmosphere.

It might seem trivial but this lies at the heart of the SRH conception. A SRH Universe is unlimited just as Cantor showed that the sets of numbers are unlimited—that is not just that the numbers in each set is unlimited by the sets of infinities is unlimited in a way that can’t be grasped by any set! A fractal that extends in both directions with an infinite hierarchy of scale going upwards and downwards—the proper conception of Universe is something that in its very nature is ungraspable. The SRH says why very simply—if a body of understanding ever did try to grasp the scale of the Universe it would always need something outside itself in order to say something meaningful about itself. It cannot by the SRH ever say anything meaningful about its own existence, because that is a given from which the theory necessarily already depends rather than explains.

QED

Technorati Tags: Multiverse,Universe,Absolute,Self,Theory of Everything

SRH + Time

Ideas forming. The SRH depends upon a type of relativity. It says that any entity lives within a unique ontology where it is a given that it exists. In other words it can never be the case that it doesn’t exist within its own “frame of reference”.

This hierarchy is the same as we see with a brain scientist looking at their own brain patterns. Whatever they conclude “objectively” depends a priori upon what they experience “subjectively”. If they find a pattern that corresponds to them thinking they must realise that their conclusions are based upon the perspective of everyone else, not upon their own perspective. Within their own perspective it is rather pointless the conclude that they are thinking from the image, since “thinking” was what they had to be able to identify anyway in order to determine the correspondence between image and “thinking” in the first place.

Now, as is well documented, this is all a linguistic feature since patients can only inform scientists that they are “thinking” through language. The correspondence is between events in the body and things said, between phenomena and mysteriously the meaning of what is said (which is somehow for materialists an unexamined, unexplained, given). Typically scientists rarely question that what they are doing, and how they understand it, is within a prior world of language so they can only imagine that their experiments are somehow mysteriously beyond language. In reality language and culture precedes their enquiries. This hierarchy is the SRH also as above. As an aside I mused recently that “myth” which we attribute to the ancient stories is just as active and important today, it is just that the wealth of phenomena and facts that we weave together with myth today is so much denser. We have facts on everything and so the stories are that much more convoluted to account for all these details.

Finally the relevance to Time. We can never be outside our own time frame. Whichever time we end up in, be that Past, Present or Future for us it will be just our own time frame—it will always be Today in other words. Just as an entity cannot meaningfully make a statement about its own existence, it cannot, it seems, make a meaningful statement about its Time either. Time, like existence, only happens through the eyes of someone else for whom we may be dead or for whom we have been gone a long time. To explain the death of my grandfather to my young sister my parents said that he had gone on a long trip. There is little difference. The point is that these things are only meaningful to someone else, necessarily never ourselves. So the idea of Time travel actually contradicts the nature of Time. If I travelled in time it would mean nothing to me, in reality it would still be Today when I arrived. What would be different would be my memories and expectations. I would have memories of things that hadn’t happened yet and would have the habits of the world I left. I wouldn’t be able to meet the people I remembered and might not know the language or the customs if it was a long time before for example. However while everything might have changed it is still Today and the Time in my frame of reference hasn’t changed. Only by finding out the year from someone else and comparing with my memory of the year (which I was told before I left)  would I be able to say that I had time travelled. But this is just language not reality; it is only what other people would say.

Now does this shed light on the murder paradox? Can’t see it for now…

Snakes

Wonderful day’s snake watching in Berkshire - March 20th 2011

Technorati Tags: snake,herpitology,adder,nature

. Particularly nice female adder fresh from hibernation in expert hands (not mine).

   

Snake Watching in Sevenoaks (8th May 2011) – 3 juvenile grass snakes (pic 1 & 2 same individual)

   

Grass Snake (male): fresh from hibernation (Reading April 2010)

 

SRH (summary) and Time

Technorati Tags: God,proof,meaning,cogito,self,existence

The SRH is purely linguistic. There are no contradictions in reality—things just are—problems only occur when we try to assert things one way and then change our mind. The reader is left unsure what we mean and complains.

To summarise: the SRH (which needs a new name) notes that when referring to something by some description (essence) or asserting its existence one cannot then meaningfully attribute that essence or existence to the subject e.g. “(Ex) x exists”, or “(x) P(x) & Q(x) –> P(x)” respectively “there exists something which exists” or “for all x where x has quality P and quality Q it has quality P”. These tautologies sound ridiculous in logic but “all black swans are black” sounds almost meaningful and “I think therefore I exist” is famous.

To recap further the problem with these tautologies lies in their negations: they are contradictions or at least always false. Respectively above: “(x) x ¬exist”, “(Ex) P(x) & Q(x) & ¬Q(x)” that is “for all x, x doesn’t exist” and “there exists an x such that x has P, Q and doesn’t have Q”. The latter is a typical contradiction the former is a type I don’t know that i’m calling existential contradiction. The famous Descartes’ statement has this SRH problem at root: its very appeal and certainty lies in the tautology that to be thinking at all he must exist (we know what he means even if it doesn’t technically imply an existing self like entity). But the statement is misleading because its negation is an existential contradiction and so there being no situation under which it can be false (it is always true) and so fails to convey any particular meaning! We know nothing after reading it that we didn’t know before. Another way to put that is there is nothing to learn about such a sentence’s use; we can say it anytime and anywhere in any imaginable universe.

The relevant to a proof of God is firstly not to prove “(Ex) x is God” i.e. there is a thing called God. This is clearly nonsense at first sight since God made “all” things so one presumes he either made himself or he isn’t a thing. It staggers me that Dawkins et al. waste time pursuing this dead end. It makes more sense for God to be a principle (principal perhaps) namely that nothing can assert its own existence, instead depending upon other things. The name of God in the Arahamic religions is Yahweh in Hebrew which means “I AM”. It is important to realise that because of the SRH we cannot meaningfully assert this for our self. Any sense of “I am” comes from outside us.

Returning to the thread if this blog entry. The SRH and existential contradiction is linguistic. There is one famous field of existential contradiction namely time travel typified by the paradox of going back in time and killing oneself. The problem then arises was there a murder? If there was then the person who was murdered is also the murder. But if there was a murder it also means that the murderer was killed before he did the murder. However if there wasn’t a murder then what exactly did the time traveller do?

It is only an embryonic thought at this stage but similarity to the SRH signals an alarm bell that this “time travel” and indeed “time” itself may be only linguistic at root and not real. This wouldn’t be a new idea but I don’t grasp it yet. I read earlier in the year (but can’t remember where) a poem in which it is said that “self” is only a feature of our Indo-European languages and with a different language structure we would be able to avoid this cultural artefact all together.

SRH : Existential Contradiction

A month ago I had a brain wave. It occurred to me that the SRH is to do with existence.

I use the logical syntax:

(x)   : for all x it is true that
(Ex) : there exists x such that
¬ : not/negation
<statement>

Thus the proof of God is this:

The simple sentence “this sentence exists” seems unproblematic:

• <(Ex) x is this sentence>

But consider:

• <¬(Ex) x is this sentence>, or equivalently
• <(x) x is not this sentence>

These sentences are equivalent and are false because the sentence itself serves as an entity which contradicts them.

Now we can’t say that the sentences are “not sentences” because that would eliminate the entity we need to make them false. So it is not that self-reference is impossible as was naively proposed by the SRH.  However there is something odd.

The sentences are necessarily false. Once we have read the sentence we cannot then deny that the sentence exists, for what did we just read? So by the time we have understood the sentence we are already committed to its existence; we are already committed to its falsity. It is an analytic statement false by virtue of the definition of its own words. However it is a posteriori to the extent that we must have experienced it to have proof that it exists. (This is in contrast to Kant’s synthetic a priori.) It is thus a necessary contradiction.

It follows that its negation (statement 1) is not just true but necessarily true. It is a tautology, an analytic a posteriori.

So all the sentences above carry no information that the reader isn’t already familiar with by virtue of reading them. While they seem to make profound statements they are actually meaningless just as “Black swans are black” doesn’t tell us anything we didn’t already know: if we can find a black swans we already know it is black. More generally then for any predicate:

• (x) S(x) & B(x) –> B(x) 

clearly doesn’t tell us anything i.e. anything which is S and has property B has property B… i.e. all swans(S) which are black(B) are black(P).

What this means is that no entity can carry information about its existence or any feature which is required to identify it.

This means, and this is the SRH, that entities can only be meaningful about the existence of other entities apart from themselves.

To put it another way: we are very unlikely to hear that we have died and if we did we would know it was false. Thus the statement that we are alive is meaningless to us. It is this meaninglessness which means that we must be silent when it comes to issues of our self-existence and non-existence. Death, or indeed any word, doesn’t make sense here.

In contrast however other people can die and so we can make meaningful statements about their being alive or dead. When someone else makes a statement that we are alive then it is meaningful, but only from their point of view. This is social consciousness. If we attribute meaning to “I am alive” it is because we have adopted a social consciousness. This is not a good thing because why would we do this when we can see with our own eyes the truth? I suspect that the search for fame and social status derives from this weakness of our own eyes. The need to make noise and words (as I do here) is also such a weakness. For such a consciousness Death is a very real thing.

From this stems all the rest of the SRH. Most importantly that no system can exist independent of another because if it was an Ultimate theory of Everything it would need another system to state meaningfully that it did indeed existed as the ultimate system.

Likewise for every entity that seeks knowledge of its existence there is always an Other outside it that it must acknowledge first. This is the God Proof. Not the proof of a particular entity amongst all the others (the naive view of God) but the principle that there is always and necessarily an entity outside.

This also explodes the narcissistic, solipsistic world view. No self can know its existence before it knows the existence of another, and worse for the self it is the view point of the other that it adopts as its own proof of its existence! If it really looked at itself with its own eyes it would be speechless because what can its eyes “see” that his “seeing” hasn’t already told it?

Video Compression for Nokia Phone

Just compressing some files with MediaCoder and did some reading and looking at the various options. MediaCoder is a front end for the various opensource and free solutions that have emerged over the years. Have settled on the following settings after comparing various options:

Container: MP4

Audio: AAC seems better than MP3 for high compression (<44kbps variable). But >77kbps, variable, AAC versions 2 is worse than version 1 and as compression is reduced quality doesn’t increase much for either so MP3 becomes the favoured compression.

Conclusion:
For low quality TV storing am using HE-AAC V2 (Nero Encoding). Quality=15. 32kbps (voice). 44.1kHz sampling - seems to affect quality a lot if lower.
For movies MP3 (LAME), 112 Average Bit Rate i.e. cassette quality (CBR is pointless!). Original sampling.

Video: have settled on XviD (opensource version of DivX) Advanced Simple Profile Level 5 for phone, and H.264 for movie.

Conclusion:
Movie Video Quality: 90 halves video size.
Phone Quality: 80 seems to provide good quality and less than 1/4 size.

If interlaced (i.e. TV format) needs to be converted to progressive to aid compression codecs. This has bonus of removing some unneeded frames too. (Interlacing refreshes the screen in alternating lines so frames come in pairs called fields, these pairs are combined into single frames for progressive.)

Frame rate: the phone is 15fps. For movies and long video keeping original as low frame rate is tiring on eyes.

Aspect Ratio (AR). The phone is 320x240 pixels (4:3). Set Display AR for phone 4:3 but without crop squishes the picture but is watchable.

Desire is the measure of all things

Returning from a photo trip to a field where I thought I had seen a rare species of butterfly (it wasn't) I was thinking out the "value" that such a discovery would bestow on the land. Money would be available for its conservation. People would be interested in it, and desire it.

It raised and solved the hindrance I have felt with conservation since I was a child (and why I don't work in conservation at the moment)... people by definition don't want it... if they did then we wouldn't need to conserve it.

What people want is row upon row of clothes shops selling fabrics with different patterns on in essentially the same shape with minor differences which attract a lot of attention. People also want restauants which sell essentially the same 5 meats, 15-20 vegetables, 10 sea foods in a variety of combinations which also attract a lot of attention. These are a few of our favourite things but the natural environment is not very well represented and indeed the natural environment is transformed to provide the above items.

There is no intrinsic value to the rare species of butterfly, just as there is no intrinsic value to a particular cut of fabric; what is different is that people desire the particular cut of fabric more than the particular cut of butterfly.

However there is a real difference beteen the latest fashion item and a butterfly: once the butterfly is extinct there is no way to recover it. This is not a black/white point but it does press for a resolution of value.

There are two things here: matter and ideas. Traditionally ideas are free but you need to pay for the acquisition of material objects. I imagine this is a practical issue of supply. However consider a society where ideas were protected by eleborate codes of secrecy like with the Greek Mysteries and the various secret societies today e.g. Masons. In such a world we might pay large amounts of money to enter into such societies, while in a world where mass production powered by very cheap energy would provide free acquistion of goods. Alternatively if we established a culture of sharing the the latter could be achieved also. As an aside I was thinking how free bikes might work. It was tried in Amsterdam but they were all stolen by people belonging to property systems outside. It might be that badly working bikes were more common so we could cycle them to a garage and have them replaced with a working bike - this way covering the maintenance. Only the garages would need to be funded then - but could easily be operated on a voluntary basis. My mother says of all this that it is "unrealistic" and that it is a "hard world" - except that such thinking is exactly what makes and maintains it as a hard world ;-) Anyway a diversion.

Returning to the main thread the point is that the butterfly could be just as valuable as a crutial city hospital if we so desire it, or as unvaluable as a piece of litter: the point is that there is no intrinsic value.

A friend's father once invited me out of the swimming pool at his home and sat me down and asked the 17 year old me what I was planning to do. I said Zoology and conservation. He, a doctor, said couldn't I think of something more useful. This essential point has lingered in my psyche all my life; it is the question of how best to use ones life; what exactly makes a life valuable; what would it mean to live one's life well and not waste it.

Well I realise there is no absolute answer in a free monetary market: it is simply a matter of what people desire.

Beyond the market there are many arguments about life but crutially they lie outside the mechanisms of economics. The real answers to these questions cannot be understood by markets, nor then can value really be established by markets.

The Bus Problem

Having waited for many buses the question arose of why it always seems that a bus comes first on the other side of the road.

Assuming that it is the same buses running in a circle on the route then we know that the average probability of a bus on either side is the same (call it p).

However the fun occurs if there is any synchrony. Suppose that there are no delays and the buses are scheduled to arrive at 10mins past the hour (PTH) on the other side and 20 PTH on your side. In order to see your bus come first you need to arrive between 10 and 20 PTH which is only 1/6th of the time. At such a bus stop you will experience an apparent “unfairness”.

In reality buses set off on time from the depot but synchrony happens en route. The reason is that the number of passenger to board a bus is proportional to the time since the last bus, and the time spent at the stop is proportional to the number of passengers. Any delays thus feedback positively. A large party of people turning up at the stop, or someone looking for their ticket will delay the bus. It means they have more people to pick up at the next stop, and the bus behind will have caught up a bit and so have less people to pick up and so very quickly it will be following the bus in front. This is why buses never come singly (especially toward the end of the day or the bus route). This means that there is a different grouping of buses for people waiting on the outward and return routes of a bus route.

2Do…

I still need to do the maths here…

The other thing I wanted to do was use appropriate distributions to show the exact probability of n buses passing on the other side…

The Launderette problem

I once had an argument with an ex about whether it was cheaper to put all our wet clothes in one drier and run it for longer or split it between two driers and run each for less time. She thought two, I thought one. I should have known that in such heated dualistic debates there is truth in both arguments!

All the water in the clothes (above the dryness level) needs to loaded into air and removed from the dryer. First up a model of the air moisture curves from both scenarios.

Let us assume that there is a maximum water load that air through the drier can take, there is therefore a maximum rate of drying at saturation. The amount of water removed at saturation is this rate multiplied by the time at saturation.

Once the rate of evaporation of water from the clothes falls below saturation of the air then the moisture of the air will decay. I assume an exponential decay curve and some arbitrary percentage as “dryness”. The moisture in the air through the load with twice as many clothes but the same air flow one would expect to reduce at half the rate of the half-load. The area under a decay curve that starts with half some rate R is twice that of one with rate R, and also takes twice as long to reach some arbitrary level. So once the moisture falls below saturation there is no advantage to either method.

It is then easy to see that, at saturation, the remaining water (which is the same in both scenarios) will be removed in a time proportional to the amount of water. So the large load will take proportionally longer.

From this argument there is no difference between strategies. Which is easier to argue in terms of energy. The cost of any scenario is proportional to the amount of energy (electricity) put in. The length of time to dry is also proportional to the amount of energy put in, or in other words the cost.

The only variable remaining is the efficiency of drying, that is the possibility that one scenario allows for air to be “unused”. Originally I thought that putting all the clothes together increased the chance of a air coming into contact with a wet surface. However if we over-load the drier so air cannot flow between the clothes then this reduces the efficiency. On the other hand if we put just one sock in the drier then most of the air will flow through without ever coming into contact with the sock. It seems that (as usual in such arguments) we were both right and actually there is a bell curve with an optimum loading. That optimum will be around the loading where the clothes are freely spinning in the tumble drier, but not so far apart that air can pass through without good contact with the clothes.

Today is the vote for AV. First past the post is good for immediate and decisive action, but as seen in this exemplary situation above, in reality the correct action requires understanding and resolution of both sides of an argument. This is why an educated King making decisions based upon the competing input of his advisors makes the best form of government.